\subsection{{\tt{gauss}}: Gaussian Elimination\label{s:toys-gauss}}

This module solves a matrix equation $AX=V$ for
a dense, symmetric, diagonally dominant matrix $A$
and an arbitrary vector non-zero $V$
using explicit reduction.
Input matrices are required to be symmetric and diagonally dominant
in order to guarantee that there is a well-formed solution to the equation.

{\inputspec}

\begin{description}
\item[{\tt{matrix}}:]
	the real matrix $A$.
\item[{\tt{target}}:]
	the real vector $V$.
\end{description}

{\outputspec}

\begin{description}
\item[{\tt{solution}}:]
	a real vector containing the solution $X$.
\end{description}
